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{\bf ADVANCED DYNAMICS --- PHY 4241/5227}\\\vspace {2mm} 
{\bf SOLUTIONS -- SET 8}\\%
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\begin{description}

\item{(25)} One finds
$$ \pmatrix{x'^{\,1}\cr i\,x'^{\,0}\cr} = 
   \pmatrix{\cosh(\zeta)& i\,\sinh(\zeta)\cr 
        -i\,\sinh(\zeta)&    \cosh(\zeta)\cr}\, 
    \pmatrix{x^1\cr i\,x^0\cr} $$
and in components
\begin{eqnarray} \nonumber
     x'^{\,1} &=& \cosh(\zeta)\,x^1 - \sinh(\zeta)\,x^0 \\ \nonumber
  i\,x'^{\,0} &=& -i\,\sinh(\zeta)\,x^1 + i\,\cosh(\zeta)\,x^0
\end{eqnarray}
or, equivalently,
\begin{eqnarray} \nonumber
   x'^{\,0} &=& +\cosh(\zeta)\,x^0 - \sinh(\zeta)\,x^1\\ \nonumber
   x'^{\,1} &=& -\sinh(\zeta)\,x^0 + \cosh(\zeta)\,x^1 
\end{eqnarray}
$$ \pmatrix{x'^{\,1}\cr x'^{\,0}\cr} = 
   \pmatrix{\cosh(\zeta)& - \sinh(\zeta)\cr 
        - \sinh(\zeta)&    \cosh(\zeta)\cr}\, 
    \pmatrix{x^1\cr x^0\cr} $$

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